The Embedding of Meshes and Trees into Degree Four Chordal Ring Networks

In this paper a particular computer interconnection network, the symmetric chordal ring network of degree four, is presented, and the mapping of meshes and binary trees onto chordal ring networks is analysed. Expressions for the network diameter (the maximum distance a message must travel between any pair of computers) and the mean inter-computer distance are derived for a sub-set of chordal ring networks. Such networks incorporate the maximum number of computers for a given diameter, and have a communications cost, measured either as network diameter or as the mean internode distance, of O(\/N). While these networks provide attractive properties for mesh-based applications on smalland medium-sized multicomputer systems, binary trees are restricted to five levels (31 nodes).